Theseus' body, is there any part of a human that is cellularly or even atomically stagnant?

Sensitive cells in the ear (hair cells) are created once, and for life. They are notoriously non-replaceable, and if they die because the ear is exposed to a loud noise, then, well, that's it. No hearing for this set of frequencies, ever.

The reason for that is, probably, that the cochlea is so complex that it can only be built once. You can not repair it, you can only grow it. If I were to give a metaphor, it's about how Egyptian temples were built: they would bring some stones, cover them with sand, put some stones on top, cover it with sand again - and repeat it until the whole temple is built, and covered in sand. And then they would start clearing the sand, while simultaneously carving and painting the stone. A temple that is built like that can not be easily fixed or repaired, as the process of building it can be repeated only once. It's easier to build a new temple than to repair an old one.

But back to the body. Even more interestingly, there are parts of the body that need to be dead by the time we are born, or otherwise they won't work. One great example are the 3 little bones in the middle ear (the ossicles). To grow, bones should be alive, and they should have some blood flowing around them. But in the adult body these bones are surrounded by air, not by fluid of any kind, and to work properly, as mechanical amplifiers, they should be light and dry. So they die - in order for us to live. Die before we are born.

Another similar example is the lens in the eye. The lens is made of cells (like almost anything in our body), but it also needs to be transparent, and live cells are not transparent. So the cells that make up the lens die before we are born. Unlike for the ossicles, they don't die and dry out, but instead they get rid of all cellular elements, one by one, and in the last final move get rid of the nucleus itself. So now in our lenses we only have cell bodies, filled with a certain transparent stuff, and that's it. It's shells of the cells, empty shells, all for the sake of giving the body some vision.

Isn't it nice? I really like the imagery here. A small thing needs to die so that the larger entity could live. It's pretty rich in metaphor. (edit grammar)

Some cells are replaced far more slowly than others. Sperm and blood are constantly being made and destroyed but osteocytes in your bones take far longer to be replaced (>25 years). Almost every cell in your body will be replaced every decade.

Cartilage, ligaments and tendons can heal and be replaced at a cellular level however if too much damage occurs then the body cannot repair it in the same way as we can't grow back toes etc.

That's really fascinating. so yes dead cells would indeed not change in a human. I just wasn't sure we had any that never got replaced (hair/nails regrow constantly)

so i guess every 7 years you may be a new person, except for your teeth lenses and ossicles.

As other people indicated in other threads, most (almost all) of your brain cells don't ever get renewed. For a long time people thought that brain cells don't regenerate, and that's it, full stop. Now we know that there are several small pools of cells that are born during our life, and get integrated into the circuits, in some most critical parts of the brain (e.g. olfactory system, hippocampus). To take the place of their dead comrades, so to say.

Still, speaking in numbers, that's a drop in the sea. Nothing even close to a "new person every 7 years". Proteins are recycled, for sure, but cells in the brain - nope. Some patching here and there, some re-furbishing, but not more than that.

So far the only thing i can think of is teeth that would potentially be inert.

Osteocytes can live up to 25 years before the entire cell is replaced but what about at a lower level. are parts of the osteocyte itself replaced within it's own lifespan?

Good thought, the enamel on teeth is likely irreplaceable. Parts within cells will be replaced but with a cell that does so little and doesn't divide, like an osteocyte, that process would still be glacially slow. Several cell types in brain tissue don't get replaced but at a molecular level, they're likely to be repaired over time.

While your information on cellular replication is correct, in terms of physical being, this is an incomplete answer.

Even cells that do not divide still metabolize. They take in new nutrients and expel waste, rebuilding their proteins and cell membranes with new building blocks from outside the cell.

Even genetic material in a nondividing cell will still be read, and thus occasionally damaged, and thus repaired with new nucleotides. While this is an extremely slow method of 'replacement' I think it is still entirely reasonable to say everything in these nondividing cells replaces itself every few years, with the exception of DNA.

Yes, that's mostly true (as far as I know). All proteins in living cells degrade, and so are constantly recycled (with a half-life time of minutes / days / weeks) (ref). The same (at a somewhat slower rate, with a half-time from days to months) is true for lipids (ref). The DNA is probably the only part that isn't renewed (except for the reparation processes).

But I am quite ignorant on these topics, so I am half-guessing here. And also I don't know anything about, say, bones, or tendons. So if you want a real answer, we'll have to wait for a specialist =)

(edit: trying to verify my claims through googling)

As a follow up question: Even though the cells remain for life, do the metabolic processes and activities of the cell cause it to replace its molecules and atoms over time?

I.e. Are the molecules that compose the membranes replaced occasionally such that over enough time none of the original ones are likely to remain? Might it be possible that over enough time, my body would be unlikely to have any of the same atoms in it that it did many years ago?

Mostly because there's no mechanism to "fix" things - a lot of the structures are created once during development and don't have any instructions on how to fix them once they go wrong. You can't shed a limb and regrow it, so the developmental programming that sets how to build the bones can't be re-triggered.

Basically, the instructions for the human body (and most animal bodies) does not come with a troubleshooting manual, so scar tissue is the best it can do.

One last analogy: You break a fancy piece of wooden cabinetry, and the only tool at your disposal is wood-glue. What do you do when the "broken" piece is actually a hole in the side of a panel? You fill in the hole with as much of the wood as you can salvage along with a generous helping of glue, and voila: the furniture equivalent to scar tissue.

Neurons cannot be replaced once destroyed, but damaged neurons can sprout new axons and self-repair to a limited extent. Neurons are not static - the ones in your brain are always creating new connections and breaking old ones, which is the physiological foundation for things like memory.

Also, to my knowledge, the enamel of your teeth isn't something that can grow back once lost.

That was an amazing post, thank you. What are the options for replacing the whole cochlea in a transplant, rather than trying to repair parts of it?

those tags on your shoelaces are called "aglets"

Neurons might not reproduce, but you do generate new ones over time from stem cells.

Neuroscientist and Alzheimer's researcher here: this is correct. As /u/AngerTranslator noted, adult neurogenesis has been demonstrated to occur in the dentate gyrus, as well as the olfactory bulb. Additionally, there is some migration of young neurons from these areas to neighboring regions, though it is very unlikely that this pattern extends to the entire brain.

Now, to be clear, we're talking about human brains... some species of fish engage in an enormous amount of neurogenesis after maturity. So brains as a general class of organs can engage in neuron replacement throughout the lifecycle of an organism. Why it doesn't occur in humans is an interesting, if perhaps unanswerable, evolutionary question.

I think that an answer to OP's question might be more philosophical than scientific: so what if human nerve cells aren't typically replaced? The fact remains that, theoretically, if you could manage to replace all the cells in the body, bit by bit or all at once, the person who has their body being replaced would have no notion of it. This fact is more important than whether or not it actually occurs as it amounts to the same dilemma.

When cells are replaced the DNA is replicated. There are little bits of DNA at the ends of the chromosome called telomeres, which effectively act as binders (like the tags on your shoelaces) to stop the DNA unravelling. The problem we have is that our version of DNA polymerase (the enzyme that copies DNA) falls off the end just as it's about to copy the last few bases, so the telomeres get a little shorter with each replication.

It is suggested that old age is a consequence of the telomeres getting so short that eventually the DNA is not stable enough to hold itself together.

Note, this is a simplified version of events, more info here and here, also note that there are a whole bunch of enzymes involved in DNA replication, not just polymerase

There's a truth to it. A chemical that selectively kills one type of brain cells was once discovered as a contaminant for an opiod drug of abuse. Prolonged alcohol abuse kills brain regions responsible for short-term memory consolidation - not directly, but kills anyway. PCP (another drug of abuse) apparently* creates lesions in the brain.

And each time you have a concussion, even a mild concussion, millions of cells in the brain die. One season of playing american football in high school = a reduction in IQ by about 2-3 points (I can't find the original paper link, so here's some random press-release I googled).

* See the discussion below (edited for footnote)

Tendons and the lenses of the eyes are pretty stagnant, even at the atomic level. This has recently been confirmed by carbon 14 measurements of the Achilles tendons and lenses of middle-aged people. As atmospheric nuclear bomb tests released quite a lot of 14C, the atmospheric level of 14C have been dropping over the last 50 years. That means that non-renewing tissue in people in their 50's contain more 14C than renewing tissue does.

As for neurons, every component of living cells are replaced, even the DNA is replaced one damaged base at a time.

edit: source: I can only find news articles about this in Danish, and none of them have references to any scientific articles.

Every time a cell divides because its neighbor cell died and needed to be replaced, the instructions for how to make a new cell get damaged at the ends by a small amount. These DNA instructions have unneeded buffers at each end, called telomeres, that stop this damage from immediately being a problem, but that damage keeps adding up until the buffer is gone and things start going wrong.

Some parts are made by cells, but not off cells, like nails, hair, teeth, or bones.

As long as it's not as slow as a human lifespan the paradox of the riddle holds.

Though with ships or homes or other inanimate things the atoms within a brick or a plank aren't going anywhere so we can observe that transformation at a higher level. For living things even if the individual cell is present if it's been wholly replaced at a molecular or atomic level then it's a different cell and by proxy you as the whole are not the same.